All categories

3 years ago

two sides of a triangle measure to 20cm and 30cm. Which of the following could be measure by the third side

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

5 0

Answer: With no choices given here, here are a few possibilities.

If it is not a right triangle, the third side could be any number less than 50 cm

If it is a right triangle, the third side could be the hypotenuse, which would be 10√13 or about 36.05 cm.

If 30cm is the hypotenuse, the other side would be 10√5 or about 22.36 cm

Step-by-step explanation: If the two given sides add up to 50, they flatten out to a straight line, equal to the third side, so it is no longer a triangle. The third side must be less than the sum of the other two sides.

We can use the Pythagorean Theorem a² + b² = c² to calculate the lengths of the sides of a right triangle.

For example

20² + 30² = c²

400 + 900 = c²

1300 = c²

√1300 = √(100)(13) = √c²

10√13 = c ≈ 36.05

You might be interested in

Consider the diagram below which of the following represents the values of x and y?

V125BC [204]

Please show a picture of the diagram.

7 0

2 years ago

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time t > 0 is $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

$\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t$

where, $\text{R}_i_n$ = concentration of salt in the inflow $\times$ input rate of brine solution

and $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

So, $\text{R}_i_n$ = 4 lb/gal $\times$ 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

= 3 gal/min - 2 gal/min

= 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

= $\frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min}$ = $\frac{2A(t)}{500+t} \text{ lb/min }$

Now, the differential equation for the amount of salt A(t) in the tank at a time t > 0 is given by;

= $\frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }$

or $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

4 0

3 years ago

Pietro buys 20 candy bars for $6 he plans to sell all 20 candy bars in 1 day he need to make a profit of $10 per day to meet his

iren [92.7K]

He would have to charge 80 cents per candy bar!

5 0

3 years ago

Can you construct a triangle that has side lengths 2 yd, 9 yd, and 10 yd?

yan [13]

Yes

The rule to check if a triplet of numbers can represent the sides of a triangle is the following: the sum of the length of two sides must exceed the third one.

This happens for all possible couples in your case:

$2+9=11>10$

$2+10=12>9$

$9+10=19>2$

3 0

3 years ago

Give the property that justifies each step.

frosja888 [35]

Answer:

Please check the explanation below.

Step-by-step explanation:

Some of the properties are defined as:

Distributive property

$a(b+c) = ab+ac$

For example,

suppose a=3, b=4, c=5

3(4+5) = 3(4) + 3(5)

3(9) = 12+15

27 = 27

Subtraction property of Equality

if (a=b), then a-c = b-c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a-c = b-c ⇒ 2-5 = 2- 5 ⇒ -3 = -3

Addition property of Equality

if (a=b), then a+c = b+c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a+c = b+c ⇒ 2+3 = 2+3 ⇒ 5 = 5

Multiplicative property of Equality

if (a=b), then a×c = b×c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a×c = b×c ⇒ 2×5 = 2 × 5 ⇒ 10 = 10

Division property of Equality

if (a=b), then a÷c = b÷c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a÷c = b÷c ⇒ 2÷5 = 2 ÷ 3 ⇒ 2/5 = 2/5

Let us solve the given equation using the above properties.

7n-16=47 Given

7n-16+16=47+16 1) Addtion property of Equality ∵ if (a=b), then a+c = b+c

7n=63 2) simplify

n = 9 3) Division property of Equality ∵ if (a=b), then a÷c = b÷c

3 0

3 years ago